At stake is about $5 million, the difference between the $7.05 million Graham would receive for 2014 if Burbank finds that he should be paid as a franchise-tagged tight end or $12.13 million, the salary for a franchised-tagged wide receiver.

Graham claims he should be considered a wide receiver because he lined up at the position 67 percent of the time last season. The Saints say he should be considered a tight end, the position at which he was drafted in 2010 and was voted All-Pro in 2013.

The Saints and Graham could reach agreement on a new contact before Thursday or any time before July 15, when Graham must either sign his franchise tender or sit out the season.

Either side, officially the NFL Players Association and the NFL Management Council, can appeal.

Graham had 86 receptions for 1,215 yards and a league-high 16 touchdowns last season. In his four years in the league, Graham has 301 catches for 1,215 yards and 41 touchdowns.

Burbank held the hearing at a New Orleans area hotel on June 17-18. His past NFL-related arbitration rulings, including the ones for Drew Brees’ franchise status and Commissioner Roger Goodell’s authority to punish the Saints in the 2012 pay-for-performance scandal, were made in less than a week.